Telehealth helps to facilitate access to medical professionals by enabling remote medical services for the patients. These services have become gradually popular over the years with the advent of necessary technological infrastructure. The benefits of telehealth have been even more apparent since the beginning of the COVID-19 crisis, as people have become less inclined to visit doctors in person during the pandemic. In this paper, we focus on facilitating the chat sessions between a doctor and a patient. We note that the quality and efficiency of the chat experience can be critical as the demand for telehealth services increases. Accordingly, we develop a smart auto-response generation mechanism for medical conversations that helps doctors respond to consultation requests efficiently, particularly during busy sessions. We explore over 900,000 anonymous, historical online messages between doctors and patients collected over nine months. We implement clustering algorithms to identify the most frequent responses by doctors and manually label the data accordingly. We then train machine learning algorithms using this preprocessed data to generate the responses. The considered algorithm has two steps: a filtering (i.e., triggering) model to filter out infeasible patient messages and a response generator to suggest the top-3 doctor responses for the ones that successfully pass the triggering phase. The method provides an accuracy of 83.28\% for precision@3 and shows robustness to its parameters.